Difference quotient for $$$f{\left(x \right)} = 2 x - 3$$$

Find the difference quotient for $$$f{\left(x \right)} = 2 x - 3$$$.

The difference quotient is given by $$$\frac{f{\left(x + h \right)} - f{\left(x \right)}}{h}$$$.

To find $$$f{\left(x + h \right)}$$$, plug $$$x + h$$$ instead of $$$x$$$: $$$f{\left(x + h \right)} = 2 \left(x + h\right) - 3$$$.

Finally, $$$\frac{f{\left(x + h \right)} - f{\left(x \right)}}{h} = \frac{\left(2 \left(x + h\right) - 3\right) - \left(2 x - 3\right)}{h} = 2$$$.

The difference quotient for $$$f{\left(x \right)} = 2 x - 3$$$A is $$$2$$$A.